can you help me with game theory?
There is a company "A", which is the only one (monopoly) but other company "B"wants to join the business. In this case is the new company , which makes the first movement: joins or doesnīt join.
The company "A" has two option lowers prices or keeps them(accept).
If the new company"b" doesn`t join, the company "A" keeps her profit.
If the new company"b" decides to join and "A" accepts, they will share business and the profit will be 2/3 for "A" and 1/3 for "B"
If the new company"B"decides to join and "A" decides to lower prices ,they are going to lose profit 40% "A" and 20% "B"
1) I have to build a matrix, where the profit of "A" is u$ 100
2) I have to say if this is a Zero-sum matrix
Please help me and sorry if my english isnīt very good , I`m from Uruguay